\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t9\_euclid\_5 (TMdHrAHWEFyCH13pY5EwhdK1jFADkSqmUoh)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k1\_euclid\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_euclid\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_euclid\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_euclid\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k15\_euclid~np\_\_3))){\unicdbdjdcd}(k1\_rlvect\_1~(k15\_euclid~\\
np\_\_3)~X1~X0=k4\_euclid\_5~(k8\_real\_1~X0~(k1\_euclid\_5~X1))~(k8\_real\_1~\\
X0~(k2\_euclid\_5~X1))~(k8\_real\_1~X0~(k3\_euclid\_5~X1))))\end{array}
\label{hyp:ehhdpffgfhdgmgjgegpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}((k1\_euclid\_5~\\
(k4\_euclid\_5~X0~X1~X2)=X0){\unicdcdcdhd}((k2\_euclid\_5~(k4\_euclid\_5~X0~X1~X2)=\\
X1){\unicdcdcdhd}(k3\_euclid\_5~(k4\_euclid\_5~X0~X1~X2)=X2)))))\end{array}
\label{hyp:ehcdpffgfhdgmgjgegpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_numbers){\unicdcdcdhd}(v1\_xreal\_0~\\
X1)){\unicdbdjdcd}(m1\_subset\_1~(k8\_real\_1~X0~X1)~k1\_numbers)\end{array}
\label{hyp:egehpflgidpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_3))){\unicdbdjdcd}\\
(m1\_subset\_1~(k3\_euclid\_5~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgddpffgfhdgmgjgegpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_3))){\unicdbdjdcd}\\
(m1\_subset\_1~(k2\_euclid\_5~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgcdpffgfhdgmgjgegpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_3))){\unicdbdjdcd}\\
(m1\_subset\_1~(k1\_euclid\_5~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdpffgfhdgmgjgegpffd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfchfgbgmgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehjdpffgfhdgmgjgegpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k15\_euclid~np\_\_3))){\unicdbdjdcd}((k1\_euclid\_5~(k1\_rlvect\_1~\\
(k15\_euclid~np\_\_3)~X1~X0)=k8\_real\_1~X0~(k1\_euclid\_5~X1)){\unicdcdcdhd}((k2\_euclid\_5~\\
(k1\_rlvect\_1~(k15\_euclid~np\_\_3)~X1~X0)=k8\_real\_1~X0~(k2\_euclid\_5~\\
X1)){\unicdcdcdhd}(k3\_euclid\_5~(k1\_rlvect\_1~(k15\_euclid~np\_\_3)~X1~X0)=k8\_real\_1~\\
X0~(k3\_euclid\_5~X1)))))\end{array}$$
\end{theorem}
\end{document}
